Since iOS 7 came in, Apps that aren't on the screen working, go into a Nap State, and therefore don't use up your Battery.
The caveat to this, is Apps that use Location Services and its Active within a given App, or Maps or a GPS App being used in the background.
So in short the answer is No, it doesn't necessarily save you battery life at all.

Now to close them all at once, this is something we all have been wanting for quite some time. I killall command, sort of thing, but again, No !! It can't be done unless you have a JB iPhone. You have to think though, its a lot easier now to just swipe up, and quickly at that to close all of your Apps. This way, you still have the option to keep 1 or 2 open if yo want.

Dont forget to use the Reputation System if someone has helped you out !!!Arguing with a zealot is only slightly easier than tunneling through a mountain with your forehead!!!!!MoTM☆☆☆

- Too many "beachballs", read this: Beachballs- Computer seems slower than it used to? Read this for some slow computer tips: Speedup- Almost full hard drive? Some solutions. Out of Space- Apple Battery Info. Battery

In that case there is no point in quitting the apps (swiping to the top) because by leaving them in its 'nap state' its quicker to open them. Right?

Hi Simonvee - not sure if you mentioned which iDevices are being discussed, i.e. iPads vs. iPhones or both (but makes no difference w/ the same iOS) - but I agree w/ the above and the other posters - apps in 'suspended mode' use virtually none of your battery (unless as stated wireless services may be active, so a consideration).

Now, I'm not sure the apps open any sooner if closed vs. suspended, but in the latter state, your settings should be preserved, so on re-opening, the status of the app should be the same. I do some 'primitive' multi-tasking on my iPad 2 (e.g. copying from one app, then opening another) so maintaining the same status helps - hopefully in iOS 8, multi-tasking will be better addressed to alleviate some of these issues.

Thus, bottom line is to just leave the apps suspended (w/i the issues discussed). Dave